BABYL OPTIONS: -*- rmail -*- Version: 5 Labels: Note: This is the header of an rmail file. Note: If you are seeing it in rmail, Note: it means the file has no messages in it.  1, edited, forwarded,, Mail-from: From hovey@math.mit.edu Fri Feb 3 09:53:22 1995 Return-Path: Received: from nevanlinna.mit.edu by math.mit.edu (4.1/Math-2.0) id AA23567; Fri, 3 Feb 95 09:51:15 EST From: Mark Hovey Received: by nevanlinna.mit.edu; Fri, 3 Feb 95 09:51:11 EST Date: Fri, 3 Feb 95 09:51:11 EST Message-Id: <9502031451.AA21474@nevanlinna.mit.edu> To: hovey@math.mit.edu Subject: Hopf mailing list Reply-To: hovey@math.mit.edu *** EOOH *** Return-Path: From: Mark Hovey Date: Thu, 9 Mar 95 09:51:11 EST To: hovey@math.mit.edu Subject: Hopf mailing list Reply-To: hovey@math.mit.edu This is the fifth installment of a mailing list of algebraic topology papers recently uploaded to Clarence Wilkerson's archive. Instructions at the end. Mark Hovey Papers uploaded to Hopf between Feb. 17 and Mar. 9, 1995: 1. /pub/Aguade-Broto-Notbohm/cookemod2.abstract A mod two analogue of a conjecture of Cooke by J. Aguad\'e, C. Broto and D. Notbohm Abstract: We study spaces whose mod 2 cohomology has the form: Poly(x)\otimes Exterior(Sq^1x). We prove: Theorem: There is a space X with this cohomology if and only if x has degree 2, 4 or 8. The 'only if' part can be considered as the mod 2 version of a conjecture of Cooke. Its proof is similar to the proof for old primes (contained in Cooke.dvi) but one should be slightly more careful in small degrees. The most interesting goal of this paper is probably the construction of what we think to be remarkable space X with H*(X;F_2) = F_2[x_8] \otimes E(Sq^1x_8) 2. /pub/Boardman/stabop.abstract DVI FILE: stabop.dvi TITLE: Stable operations in generalized cohomology AUTHOR: J. Michael Boardman TO APPEAR: Handbook of Algebraic Topology, ed. I.M.James, Elsevier (Amsterdam, 1995). We describe the structure of the stable operations on E-cohomology following Adams, in a manner that generalizes to unstable operations. The appropriate context is the language of comonads and coalgebras over a comonad. The necessary category theory is developed in detail. Five examples are presented: ordinary mod p cohomology, unitary cobordism MU, Brown- Peterson cohomology BP, complex K-theory KU, and Morava K-theory K(n). 3. /pub/Boardman-Johnson-Wilson/bjw.abs DVI FILE: bjw.dvi TITLE: Unstable operations in generalized cohomology AUTHORS: J. Michael Boardman, David Copeland Johnson, W. Stephen Wilson TO APPEAR: Handbook of Algebraic Topology, ed. I.M.James, Elsevier (Amsterdam, 1995). We describe the structure of the unstable operations on E-cohomology in terms of comonads, in the style of the companion paper on stable operations. There are two variants, depending on whether we consider only the additive operations, or all unstable operations. For practical use, we unpack the comonad information and express it in terms of Hopf rings. Five examples are discussed: ordinary mod p cohomology, unitary cobordism MU, Brown-Peterson BP-cohomology, complex K-theory KU, and Morava K-theory K(n). We give two applications to BP-cohomology. The first shows that the presence of unstable operations imposes dimensional restrictions on the Landweber filtration of the BP-cohomology of a finite complex. The second constructs idempotent operations in degree k that recover the known unstable splittings of BP-cohomology. 4. /pub/Shipley/convergence.new (This is a significantly revised version of a paper already on the archive. I reproduce here an abstract followed by a brief description of the changes--Mark.) We produce new convergence conditions for the homology spectral sequence of a cosimplicial space by requiring that each codegree of the cosimplicial space has finite type mod $p$ homology. Specifically, we find conditions which ensure strong convergence if and only if the total space has $p$-good components. We also find exotic convergence conditions for cosimplicial spaces not covered by the strong convergence conditions. These results give new convergence conditions, for example, for the Eilenberg-Moore spectral sequence and for mapping spaces. This new version contains several generalizations of the old results. Specifically, the requirement of a non-empty total space is no longer needed. Also, Corollary 10.3 is a new strong convergence result requiring p-complete codegrees instead of p-nilpotent codegrees. Of course, there have been other minor changes and corrections. 5. /pub/MWeiss/betticurv.abstract Curvature and Finite Domination, by Michael Weiss. Abstract. Gromov obtained an upper bound on the Betti numbers of a closed Riemannian manifold in terms of a lower bound on the sectional curvature. It is shown that Gromov's upper bound is an upper bound on the minimum number of cells in CW-spaces dominating the manifold. 6. /pub/MWeiss/embed.abstract Calculus of Embeddings, by Michael Weiss Abstract. This is a study of spaces of smooth embeddings emb(M,N) in the spirit of immersion theory, and in the spirit of "Calculus". It leads to very efficient calculations of emb(M,N) when dim(M) is small compared to dim(N). Immersion theory appears as the "first derivative" of embedding theory, and the game is to find the higher derivatives, i.e. the "Taylor Series". The Taylor series converges when the codimension, dim(N)-dim(M), is at least 3. This follows from a multiple disjunction lemma proved recently by Goodwillie (not in his thesis). It's an announcement - no proofs. 7. /pub/MWeiss/ortho.abstract Orthogonal Calculus, by Michael Weiss Abstract. Orthogonal calculus is a way to explore spaces equipped with a filtration indexed by the finite dimensional linear subspaces V of an infinite dimensional euclidean space. Example: BO, filtered by subspaces BO(V), or BTOP, filtered by subspaces BTOP(V). Those who like to split big spaces may be interested, and the hardy ones who still like surgery theory may also be interested, since many of the moduli spaces in surgery theory come with such a filtration. Orthogonal calculus is modelled on Goodwillie calculus: Among the spaces equipped with a filtration of the type above, some are "polynomial of degree n", and the game is to approximate arbitrary ones by polynomial ones (Taylor approximation). First order approximations in orthogonal calculus have been used heavily by Bruce Williams and me in papers related to surgery. They look like generalized total Stiefel-Whitney classes, and second order approximations look like generalized total Pontryagin classes plus generalized total Stiefel-Whitney classes. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to hovey@math.mit.edu with your e-mail address and name. Please make sure I am using the correct e-mail address for you. To get the papers listed above, point your WWW client (Mosaic, Netscape) to http://hopf.math.purdue.edu/pub/hopf.html. There are links to conference announcements, Purdue seminars, and other math related things on this page as well. You can also use ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer an abstract as well. To do this take the TeX file and save the abstract to a different file, without any \begin{document} commands or anything, and transfer that file. You can use ascii instead of binary for this. I am solely responsible for this mailing list---don't send complaints about it to Clarence. Thanks to Clarence for creating and maintaining the archive. BABYL OPTIONS: -*- rmail -*- Version: 5 Labels: Note: This is the header of an rmail file. Note: If you are seeing it in rmail, Note: it means the file has no messages in it.